| dc.contributor.author | Belton, Alexander | |
| dc.contributor.author | Guillot, Dominique | |
| dc.contributor.author | Khare, Apoorva | |
| dc.contributor.author | Putinar, Mihai | |
| dc.date.accessioned | 2026-09-23T11:28:16Z | |
| dc.date.available | 2026-09-23T11:28:16Z | |
| dc.date.issued | 2026-09 | |
| dc.identifier.uri | https://publications.mfo.de/handle/mfo/4466 | |
| dc.description | [MSC 2020] 15B99; 15A18; 46C20; 51M10; 60G51 | |
| dc.description.abstract | We obtain a complete description of the class of entrywise preservers of Lorentz-Gram matrices. This resolves, for the case of constant negative curvature, the classification of entrywise preservers obtained by Schoenberg in the zero-curvature (Euclidean) and constant-positive-curvature (spherical) settings. These preservers admit a Lévy-Khintchine-type representation and their asymptotic characteristics are related to Krein’s classification of screw lines in Lobachevsky space. Connections with complete Nevanlinna-Pick kernels and Bochner subordination are also obtained. | en_US |
| dc.description.sponsorship | Acknowledgements. The authors thank the Mathematisches Forschungsinstitut Oberwolfach for support and hospitality via the Equivariant-kernel transforms and Schur functions project within its Research Fellows programme, where work on this paper was initiated. AB thanks the Isaac Newton Institute for Mathematical Sciences, Cambridge, for the support and hospitality of its Retreats programme, where further
work on this paper was undertaken via EPSRC grant EP/Z000580/1. DG was partially supported by NSF grant #2350067. AK acknowledges support from the Government of India via an ARG grant (ANRF/ARG/2025/011665/MS) from ANRF, a Shanti Swarup Bhatnagar Award from CSIR and the DST FIST program-2021 TPN-700661. Mihai Putinar was partially supported by a Simons Foundation collaboration grant.
Claude Opus 4.8, Opus 5 and Fable 5 were used to support the development of some of the working in Sections 3 to 7 and the appendix. The authors have verified the content
of all AI-assisted material, including all references and mathematical claims, and take full responsibility for the content of this paper. | |
| dc.language.iso | en | en_US |
| dc.publisher | Mathematisches Forschungsinstitut Oberwolfach | en_US |
| dc.relation.ispartofseries | Oberwolfach Preprints;2026-07 | |
| dc.subject | Hyperbolic space | en_US |
| dc.subject | Hyperboloid model | en_US |
| dc.subject | Lorentz-Gram matrix | en_US |
| dc.subject | Entrywise preserver | en_US |
| dc.subject | Screw line | en_US |
| dc.subject | Lévy measure | en_US |
| dc.subject | Lévy-Khintchine representation | en_US |
| dc.subject | Bernstein function | en_US |
| dc.subject | Conditionally negative kernel | en_US |
| dc.subject | Nevanlinna-Pick kernel | en_US |
| dc.subject | Fractional Ornstein-Uhlenbeck field | en_US |
| dc.subject | Bochner subordination | en_US |
| dc.title | Distance Preservers for Lobachevsky Space | en_US |
| dc.type | Preprint | en_US |
| dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | de |
| dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | en |
| dc.identifier.doi | 10.14760/OWP-2026-07 | |
| local.scientificprogram | OWRF 2025 | en_US |
| local.series.id | OWP-2026-07 | en_US |
| local.subject.msc | 15 | en_US |
| local.subject.msc | 46 | en_US |
| local.subject.msc | 51 | en_US |
| local.subject.msc | 60 | en_US |
| dc.identifier.ppn | 1987085949 | |
